J.-B. Bru, V. A. Zagrebnov Exactly soluble model with two kinds of Bose-Einstein condensations (110K, LATeX 2e) ABSTRACT. We present a simple exactly soluble model which manifests two kinds of Bose-Einstein condensations, a non-conventional one due to a diagonal perturbation of the perfect Bose-gas and a conventional one corresponding to the standard mechanism of saturation.